How to satisfyingly conclude character arcs?

I'm having trouble ending my story and figuring out where my characters will end up. The protagonist is kind of a well-meaning but incompetent guy turned into a competent anti-villain. He's conflicted between giving into his "villainous" urges and redeeming himself. There's more characters and arcs I'm having trouble with too, so in general what do you think makes a good end to character development?

Do you think circularity is good? (Where the character ends up in a similar place to where they began) or will that cheapen all they've been through?

Its hard to know without knowing your story arcs. But does every character arc need to end? Unless the stories are complicated, I imagine most can end without the reader knowing. The complicated arcs only you should know the answer whether that be death, romance or whatever.

I agree that it really will depend somewhat on your story and the characters involved, but there is no set reason you have to complete a character arc completely. The anti-villain does not need to return to being a hard-core crook, nor find full redemption either.

I can't think of many books I've read where I've not had questions about where the story would go and what might happen to the characters after the tale ends. So you don't always need to make a neat bow with everything, but you also don't want to really leave everything in a huge knot that leaves the readers with far too many questions and unhappy feelings. The only way you can leave a lot of questions I think is when you plan for more books with the same characters.

At the risk of sounding like a jerk, this is your story and you have to write it. Think about what character arcs would be satisfying to you. Don't worry about making others happy when you write. If you try to cater to everyone your story will be a huge mess. Hope that helps.

I think circularity is only good in specific circumstances. It seems like more of a philosophical ending than anything else, that poses the fundamental questions of who we are and why we are who we are. If a character goes through a grand adventure, experiences a lot, grows a lot, makes hard decisions, experiences great loss and great success, et cetera, but ends up where they were in the beginning, what does that mean? Maybe I'm making more of this than I should but it strikes me that way. And I suck at philosophy so I know I couldn't pull this off!

I agree with the general consensus regarding story arcs. Why does everything need to be tied up? Why does it have to be black and white? Villains don't have to be evil, they just have to have different goals in mind than a hero. They don't even have to pursue that goal through questionable means, though the pursuit of a good and beneficial end through bad means is a fun story. You could easily leave it up in the air about his future and let your readers wonder about where he goes, maybe picking apart details in your story for clues as to his fate. There's also a lot of dependence on whether you're going to write about this guy in the future. Maybe we're just doomed to find out what he does in the future.

Do you think circularity is good? (Where the character ends up in a similar place to where they began) or will that cheapen all they've been through?

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Personally? I LOVE this sort of ending. Always have. Not sure why. There is that little click of recognition that a cycle has been completed. Presumably the character and circumstances have changed during the course of the story, or at least has been given opportunities to change, so the implication is often that this circularity represents a new start.

My favourite example in books I've read recently, is what happens to the character Logen Ninefingers in Joe Abercrombie's First Law trilogy. Don't want to spoil it for people who haven't read the trilogy yet (and if you love fantasy, adventure, satire, you certainly should) but let's say Logen finds himself in a similar physical situation at both ends of the trilogy. In a way, it's vindication for his life. Loved it.